Roots: square and cube roots and their signs
Count the numbers that square to a positive number, see why a negative has no real square root but does have a cube root, and why the root of a square is the absolute value.
π Start here: read the steps of the βLessonβ in order (1, 2, 3 β¦) and answer each question. Then continue with βPracticeβ.
- Germany: grade 9
- Iran: grade 9
Guide
3^2 and (-3)^2 are both 9, so 9 has two square roots, 3 and -3. The symbol β9 gives only the positive one (β9 = 3); the negative one is written -β9.
The square root of zero is zero. A negative number has no square root in the real numbers, since no number squares to a negative.
Every number, positive or negative, has exactly one cube root: β8 = 2 and β(-8) = -2, since (-2)^3 = -8.
The root of a square is the absolute value: β(a^2) = |a|. So β((-5)^2) = 5, not -5.